A Variational Framework for Image Denoising Based on Fractional-order Derivatives

In this paper, we propose a variational framework for noise removal by combining different fractional order derivatives. In smooth regions, we use the regularization with the fractional order greater than 2 to effectively remove the noise and avoid the staircase effect; in the region of image edges, we use the regularization with the fractional order that lies in (0,1] to better preserve them. A main advantage of this framework is the superiority in eliminating the staircase effect and dealing with better textures and repetitive structures. A set of experiments will be given to demonstrate the advantages of the proposed method.